Layer having a non-linear taper and method of fabrication

ABSTRACT

A method for forming a non-linear thickness-profile in a first layer of a first material is disclosed. The method comprises forming an accelerator layer of a second material on the first layer and forming a mask layer disposed on the accelerator layer, wherein the mask layer enables the accelerator layer to expose the first layer to a first etchant in a first region, where the exposure time for each point along a first axis varies non-linearly as a function of distance from a first point on the first axis. Since the time for which the first layer is exposed to the first etch in the first region is non-linear, the thickness of the first layer in the first region changes non-linearly along the first axis.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional patent application of co-pending U.S.patent application Ser. No. 14/270,014, filed May 5, 2014, entitled“Layer Having a Non-linear Taper and Method of Fabrication,” which is acontinuation-in-part of U.S. patent application Ser. No. 13/451,957 (nowU.S. Pat. No. 8,718,432), filed Apr. 20, 2012, entitled “Method forForming a Spotsize Converter,” which claims the benefit of U.S.Provisional Application Ser. No. 61/477,960, filed Apr. 21, 2011,entitled “Surface waveguide-based Spot-size Converter,” each of which isincorporated by reference.

FIELD OF THE INVENTION

The present invention relates to guided-wave optics in general, and,more particularly, to planar lightwave circuits.

BACKGROUND OF THE INVENTION

A surface waveguide is a light pipe that is formed on a surface of asubstrate. Surface waveguides are operative for guiding light signalsalong paths that can include curves, loops, etc. without a significantloss of optical energy. Typically, a surface waveguide includes acentral core of substantially transparent material that is surrounded bycladding material whose refractive index that is lower than that of thecore material. This refractive index difference gives rise to most ofthe optical energy of the signal being contained within the surfacewaveguide core.

Surface waveguides are typically formed on rigid substrates, such asglass or silicon. Often, multiple surface waveguides are formed on asingle substrate to collectively define a planar lightwave circuit(PLC). Surface waveguides can be configured to define complexstructures, such as ring resonators, 1×N couplers and splitters (where Ncan be 2, 3, or more), and the like, which are difficult to realizeusing conventional optical fibers.

The “mode” of the light signal propagates primarily within the core,although a portion (commonly referred to as the “evanescent field”)extends into the cladding. The shape of the mode and the size of theevanescent field depend strongly on the design of the surface waveguide.Factors such as surface-waveguide design (i.e., cross-sectional shape),index contrast (i.e., the effective refractive-index difference betweenthe core and cladding), core size, and cladding thickness all impact howstrongly optical energy is confined in the core, as well as the shapeand size of the optical mode (i.e., mode profile and mode-field size).

In surface waveguides having only a small difference between therefractive indices (or effective refractive indices) of the core andcladding material (referred to herein as “low-contrast waveguides”),light is loosely confined in the core and the evanescent field isrelatively large. The optical propagation loss of such surfacewaveguides can be very low; therefore, low-contrast waveguides arepreferred in applications where low propagation loss is critical, suchas for transmission in optical telecom or datacom systems.

Low-contrast waveguides typically exhibit optical propagation loss thatis somewhat higher than that of a typical communications-grade opticalfibers, but can also enable low-loss surface waveguide crossings,optical power splitting, and optical power coupling, which are difficultto achieve using optical fibers. Unfortunately, because they onlyloosely confine light signals, low-contrast waveguides are susceptibleto severe losses at surface waveguide bends, as well as disruption fromoptical signals propagating in other low-contrast waveguides locatednearby. Low-contrast waveguides, therefore, require large bending radiiand are not well suited for use in high-density PLCs. As a result,low-contrast waveguide systems require a large chip area, whichincreases their cost. It is possible to design a low-contrast waveguidehaving a propagation mode that substantially matches the mode profileand mode-field size of an optical fiber, however. This can reduceoptical loss that arises when a light signal is transferred between thesurface waveguide and the optical fiber. They are attractive, therefore,for combined systems where a low-contrast waveguide is optically coupledwith an optical fiber to add functionality to a low-loss optical system.

A surface waveguide having a large difference between the refractiveindices (or effective refractive indices) of their core and claddingmaterials (referred to herein as a “high-contrast waveguide”) tightlyconfines a light signal in its core such that the evanescent field isrelatively small. This enables high-contrast waveguides to haveextremely small bending radii. High-contrast waveguides can also belocated quite close to other high-contrast waveguides without incurringsignificant signal interference or degradation. As a result,high-contrast waveguides enable complex circuit functionality in arelatively small chip area and are well suited to large-scaleintegration PLCs having densely packed surface waveguides.

Unfortunately, high-contrast waveguides typically have relatively higheroptical propagation loss. Their use, therefore, has historically beenlimited to applications in which functionality is more important thanlow loss, such as sensors, power splitters, and the like. In addition,the mode profile of a high-contrast waveguide is not well matched tothat of an optical fiber; therefore, the optical loss that arises when alight signal is transferred between a high-contrast waveguide and anoptical fiber is typically quite large. As a result, high-contrastwaveguides are not well suited for combined systems where ahigh-contrast waveguide is optically coupled with an optical fiber.

In some cases, it is desirable to have both high-contrast surfacewaveguides and low-contrast surface waveguides in the same PLC. One wayto enable this is through the use of a spotsize converter, sometimesreferred to as a mode-field converter. In addition, a spotsize convertercan enable the use of a high-contrast surface-waveguide-based PLC with aconventional optical fiber by changing the mode profile of thehigh-contrast surface waveguide at its input and/or output to moreclosely match the mode profile of the optical fiber, thereby reducingfiber-to-chip coupling loss.

Attempts to form PLC-based spotsize converters in the prior art havetypically relied on surface waveguide regions comprising aone-dimensional taper in the lateral dimension, wherein the lateraltaper is formed using conventional photolithography and etching.Examples of such devices are described in “Optical spotsize converterusing narrow laterally tapered surface waveguide for Planar LightwaveCircuits,”J. Lightwave Tech., Vol. 22, pp. 833-839 (2004). While someimprovement in coupling performance is achieved with this approach, theperformance and flexibility of these devices is limited because themode-field is only controlled in one dimension.

Silicon-core surface waveguides having tapered cores have also beeninvestigated in the prior art, such as is described in “Spotsizeconverters for rib-type silicon photonic wire surface waveguides,”Proceedings of the 5^(th) International Conference on Group IVPhotonics, Sorrento, Italy, September 17-19, pp. 200-202 (2008) and “Lowloss shallow-ridge silicon surface waveguides,” Optics Express, Vol. 18,No. 14, pp. 14474-14479 (2010). Unfortunately, while the promise ofcompatibility with conventional integrated circuits is attractive, theoperating wavelengths and propagation losses for silicon-core surfacewaveguides limit their use in many applications.

In similar fashion, optical coupling between an optical fiber and aphotonic crystal surface waveguide via a laterally tapered silicon-wiresurface waveguide region was demonstrated in “Spotsize converter ofPhotonic Crystal Surface waveguide,” NTT Technical Review, Vol. 2, pp.36-47 (2004).

Of more promise, however, are mode-field conversion regions formed insurface waveguides that are tapered in two dimensions, such as describedin “Low-Loss Compact Arrayed Surface waveguide Grating with Spot-sizeConverter Fabricated by a Shadow-Mask Etching Technique,” Electronicsand Telecommunications Research Institute (ETRI) Journal, Vol. 27, No.1, pp. 89-94 (2005). While the structure of these spotsize convertersshows great promise for low fiber-to-chip coupling losses, shadow-masketching is extremely difficult to control. As a result, spotsizeconverters fabricated in this manner are expensive to produce in volumeand are likely to suffer from variations in performance as well, makingthem difficult, at best, to commercialize.

An improved method forming low-cost, commercially viable spotsizeconverters that are operable over a wide range of wavelengths would,therefore, be highly desirable.

SUMMARY OF THE INVENTION

The present invention enables a surface waveguide-based spotsizeconverter having a mode-transition region that has a non-linearthickness profile, wherein the mode-transition region is shaped via asimple and controllable tapering technique that is commercially viable.Embodiments of the present invention are well suited for use in low-lossfiber-to-chip couplers, stand-alone spotsize converters, andfiber-to-fiber optical couplers, as well as for use within a PLC toadiabatically couple surface waveguide regions having different indexcontrast.

A spotsize converter in accordance with the present invention comprisesa first region having a first mode-field size, a second region having asecond mode-field size, and a mode-transition region that opticallycouples the first and second region, wherein the transition region istapered in the vertical dimension such that the thickness of at leastone of its constituent layers changes monotonically along the lengthbetween the first and second regions.

In an illustrative embodiment, a tapered transition region is formed viaan accelerator layer that etches laterally in an etchant. Theaccelerator layer is disposed on a surface of an underlying first layer,whose material is also etched by the etchant. A mask layer is formed onthe top surface of the accelerator layer, wherein the mask includes ashaped region and a field region that are aligned along a first axis.The shaped region includes opposing sides that meet at an initial pointon the first axis and move away from the first axis in non-linearfashion as a function of distance along the first axis. When exposed tothe etchant, a lateral etch front proceeds normally inward from eachpoint on the sides, undercutting the mask layer in the shaped region. Asthe lateral etch front proceeds under the mask layer, an increasingamount of the surface of the first layer is exposed to the etchant. Thisresults in a thickness change in the first layer that varies as afunction of distance from the sides, as well as the distance along thefirst axis. The thickness profile is controlled by controlling therelative etch rates of the materials of the accelerator layer and thefirst layer in the etchant, as well as the shape of the sides.

The illustrative embodiment of the present invention comprises a ridgewaveguide having a first region, second region, and third region that isbetween the first region and second region. The surface waveguidecomprises a core of silicon nitride that surrounded by silicon dioxide.The core has a thickness in the first region that is approximately 65nanometers (nm). The core has a thickness in the second region that isapproximately 220 nm. The thickness of the core in the third regionchanges in substantially sinusoidal fashion from 65 nm where it meetsthe first region to 220 nm where the outer core meets the second region.The width of the core also changes along the length of the third regionfrom a width of approximately 65 nm wherein the third region abuts thefirst region to a width of approximately 1 micron where the third regionabuts the second region. In some embodiments, the width also changessubstantially sinusoidally in the third region. In some embodiments, thewidth of the core remains substantially uniform through all threeregions.

An embodiment of the present invention is a method comprising: providinga first layer of a first material, wherein the first material etches ata first etch rate in a first etchant; providing an accelerator layerdisposed on the first layer, the accelerator layer comprising a secondmaterial, wherein the second material etches at a second etch rate inthe first etchant; providing a mask layer that is disposed on theaccelerator layer, the mask layer comprising a field region and a shapedregion that abuts the field region at a first end and extends from thefield region along a first axis to a tip, the shaped region havingopposing first and second sides that meet at the tip, wherein the firstand second sides collectively define a first width that increasesnonlinearly from the tip to the first end; laterally etching theaccelerator layer in the first etchant such that the shaped region isundercut along directions normal to each point on the first side andsecond side; and etching the first layer in the first region in thefirst etchant such that the thickness of the first layer increasesnonlinearly from the tip to the first end.

Another embodiment of the present invention is a composition comprising:a first layer having a first region, second region, and third regionthat is between the first region and second region, wherein the thirdregion abuts the first region at a first point along a first axis, andwherein the third region abuts the second region at a second point alongthe first axis; wherein the first layer has a first thickness in thefirst region, a second thickness in the second region, and a thicknessin the third region that changes in non-linear fashion between the firstpoint and the second point.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic drawing of a side view of a ramp formed viaan exemplary accelerator-layer tapering process.

FIGS. 2A-C depict schematic drawings of side views of a substrate regioncomprising a tapered region at different points during an exemplaryaccelerator-layer tapering process.

FIG. 3 depicts operations of an exemplary one-dimensionalaccelerator-layer tapering process.

FIGS. 4A and 4B depict schematic drawings of top and side views,respectively, of a surface waveguide core of a spotsize converter havinga double-angle taper thickness profile.

FIG. 5A depicts a plot of taper profile for an exemplary spotsizeconverter having a double-angle taper region.

FIG. 5B depicts a plot of mode-profile angles induced by an exemplarydouble-angle taper region.

FIG. 5C depicts a plot of mode-profile angles induced by an exemplarysingle-angle taper region.

FIGS. 6A-B depict schematic drawings of side and top views,respectively, of a spotsize converter having a substantiallysinusoidally tapered core layer in accordance with an illustrativeembodiment of the present invention.

FIG. 7 depicts operations of a method suitable for forming a spotsizeconverter in accordance with the illustrative embodiment.

FIGS. 8A-D depict schematic drawings of views of spotsize converter 600at different points in its fabrication.

FIG. 9 depicts operations of a method suitable for determining the shapeof opening 810 in accordance with the illustrative embodiment of thepresent invention.

FIGS. 10A-B depict plots of the magnitude of etch-front angle φ as afunction of distance, z, for taper regions having lengths of 2 mm and 1mm, respectively.

FIGS. 11A-B depict plots of the thickness of exemplary core layers 610as a function of distance, z, for taper regions having lengths of 2 mmand 1 mm, respectively.

FIGS. 11C-D depict plots of the taper angle, θ, of exemplary core layers610 as a function of distance, z, for taper regions having lengths of 2mm and 1 mm, respectively.

FIGS. 12A and 12B depict plots of a mode profile induced by exemplarysinusoidal taper regions having lengths of approximately 2 mm and 1 mm,respectively.

DETAILED DESCRIPTION

The following terms are defined for use in this Specification, includingthe appended claims:

-   -   Disposed on or Formed on is defined as “exists on” an underlying        material or layer. A first layer can be disposed on a second        layer with intermediate layers, such as transitional layers,        separating the first layer and second layer. For example, if a        material is described to be “disposed (or grown) on a        substrate,” this can mean that either (1) the material is in        intimate contact with the substrate; or (2) the material is in        contact with one or more intermediate layers that reside on the        substrate.    -   Monotonically is defined as only increasing or decreasing. In        other words, the first derivative of a monotonically changing        function never changes sign. For example, a layer whose        thickness increases monotonically along a first direction has a        thickness that never decreases along the first direction. It        should be noted that the thickness of a layer can change in        either a linear or non-linear fashion and still be considered to        be changing monotonically.    -   Low-contrast region is defined as a region of a planar-lightwave        circuit comprising one or more low-contrast waveguides.    -   High-contrast region is defined as a region of a        planar-lightwave circuit comprising one or more high-contrast        waveguides.

As discussed in U.S. patent application Ser. No. 13/451,957 (i.e., theparent application), the design parameters of a surface waveguide (i.e.,cross-sectional shape, core size, core and cladding materials, indexcontrast, cladding thickness, etc. dictate the mode propagationcharacteristics of the surface waveguide. (i.e., mode profile,mode-field size, mode confinement, etc.). As a result, a spot-sizeconverter can be formed by changing one or more of these parametersalong a transition region within a surface waveguide such that the modepropagation characteristics (e.g., mode profile, mode-field size, etc.)of the surface waveguide can be converted from one configuration toanother.

Prior-art spot-size converters, and the methods by which they are made,have several drawbacks, however. For example, prior-art fabricationmethods are very difficult to control and reproduce and, therefore, arenot well suited for high-volume commercial use. Still further, thesemethods are limited to formation of only substantially linear taperregions.

In addition, the length of the transition region in a prior-art spotsizeconverter is often limited by the methods used to form it. Taper lengthis an important parameter for achieving adiabatic mode-conversion;therefore, this constrains the range of design for surface waveguidesincluded in prior-art spotsize converters.

The parent application, however, disclosed an accelerator-layer taperingmethod suitable for forming one- or two-dimensional taper regions in amaterial layer. Before describing the present invention, it will beinstructive to provide a brief example of the formation of a linear ramp(i.e., a one-dimensional taper) using accelerator-layer tapering.Additional details regarding the accelerator-layer tapering method, forboth 1D and 2D structures, can be found in the parent application.

Accelerator-Layer Tapering Process

FIG. 1 depicts a schematic drawing of a side view of a ramp formed viaan exemplary accelerator-layer tapering process. Substrate region 100includes regions 102, 104, and 106, each of which includes substrate 108and layer 110. Region 104 extends from first end 112, where it abutsregion 102, to second end 114, where it abuts region 106.

FIGS. 2A-C depict schematic drawings of side views of a substrate regioncomprising a tapered region at different points during an exemplaryaccelerator-layer tapering process.

FIG. 3 depicts operations of an exemplary one-dimensionalaccelerator-layer tapering process. FIG. 3 is described with continuingreference to FIGS. 1 and 2A-C.

Method 300 begins with operation 301, wherein accelerator layer 202 isformed on surface 206 of layer 110. Layer 110 is a planar layer ofstoichiometric silicon nitride having a thickness, h1.

Although layer 110 comprises silicon nitride in this example, it will beclear to one skilled in the art, after reading this Specification, thatthe accelerator-layer tapering process is suitable for tapering anylayer of material whose structure does not inhibit substantially uniformetch rate in all dimensions. Materials for which an accelerator-layertapering process is suitable include, without limitation, dielectrics,silicon oxides, glasses, plastics, ceramics, silicon, polysilicon,amorphous silicon, amorphous and polycrystalline silicon-containingcompounds (e.g., silicon carbide, etc.), crystalline III-V compoundsemiconductors, polycrystalline III-V compound semiconductors, amorphousIII-V compound semiconductors, crystalline II-VI compoundsemiconductors, polycrystalline II-VI compound semiconductors, amorphousII-VI compound semiconductors, metals, and composite materials.

Accelerator layer 202 comprises a sacrificial material that etches in afirst etchant that also etches the material of layer 110. Typically, thematerial of accelerator layer 202 is selected such that it etches at afaster rate in the first etchant than the material of layer 110. Oneskilled in the art will recognize that the material of accelerator layer202 is a matter of design choice and will depend on the material oflayer 110 and available etchants.

At operation 302, mask layer 204 is formed and patterned on acceleratorlayer 202. Mask layer 204 is patterned to expose surface 208 ofaccelerator layer 202 in region 102, but initially protect surface 208in regions 104 and 106. The edge of mask layer 204 is located at firstend 112 (i.e., at z=0).

FIG. 2A depicts a cross-sectional view of substrate region 100 after theformation of mask layer 204 on accelerator layer 202.

At operation 303, substrate region 100 is exposed to etchant 210 at timet(0).

Etchant 210 comprises a chemical (e.g., nitric acid, etc.) that etchesthe material of accelerator layer 202 at a faster rate than the materialof layer 110. As a result, accelerator layer 202 is removed quickly inregion 102 and etchant 210 begins to attack underlying layer 110uniformly across the region. At the same time, etchant 210 begins toetch accelerator layer 202 laterally along the z-direction from firstend 112 toward second end 114, undercutting mask layer 204 along thez-direction. In some embodiments, accelerator layer 202 is removed fromregion 102 via a different etch (preferably, a directional etch) thatremoves its material selectively over the material of layer 110. Thisensures a clean starting condition at first end 112 for the lateraletching of accelerator layer 202 in region 104. It can also improve theuniformity of the vertical etching of layer 110 in region 102.

FIG. 2B depicts a cross-sectional view of substrate region 100 duringoperation 303.

Etch front 212 moves along the z-direction at a substantially constantvelocity, thus exposing a linearly increasing amount of surface 206.

At operation 304, the etching of layer 110 by etchant 210 is stopped attime t(1). Time t(1) is selected based on the etch rate of the materialof layer 110 in etchant 210, initial thickness, h1, final thickness, h2,and the desired length, L1, of taper region 104.

Second end 114 is defined by the point at which etch front 212 isstopped in operation 204. As a result, no etching of layer 110 occurs atsecond end 114 (or beyond it in region 106) because etchant 210 has notime to attack layer 110 at surface 206. At second end 114 and in region106, therefore, layer 110 remains at its deposited thickness, h1. Atfirst end 112 and in region 102, however, etchant 210 etches layer 110for substantially the entire time period from t(0) to t(1), resulting infinal thickness, h2, for layer 110. Between first end 112 and second end114, the exposure time of layer 110 in etchant 210 is a linearlydecreasing function of distance along the z-direction from first end112. Etchant 210, therefore, creates a linearly increasing thickness oflayer 110 (from h2 to h1) from first end 112 to second end 114. Itshould be noted that the magnitude of the taper angle, θ1, is dependentupon the relative etch rates of the materials of accelerator layer 202and layer 110 in etchant 210. The relationship between θ1 and these etchrates can be described as:

$\begin{matrix}{{{\theta 1} = {\arctan\left( \frac{{ER}\; 1}{{ER}\; 2} \right)}},} & (1)\end{matrix}$where ER1 is the etch rate of the material of layer 110 and ER2 is thelateral etch rate of accelerator layer 202 in etchant 210.

One skilled in the art will recognize that the density of the materialsused in accelerator layer 202 and layer 110 impact their respective etchrates in an etchant. As a result, each etch rate can vary for the samematerial depending on how that material was formed (e.g., depositiontemperature, annealing temperature, annealing time, etc.).

FIG. 2C depicts a cross-sectional view of substrate region 100 afteroperation 304.

As further discussed in the parent application, accelerator-layertapering can be implemented so as to form regions having tapers that aremutually non-orthogonal (e.g., a beveled region or wedge), as well as,by judicious design of mask features, taper regions having non-lineartapers.

FIGS. 4A and 4B depict schematic drawings of top and side views,respectively, of a surface waveguide core of a spotsize converter havinga double-angle taper thickness profile. Surface waveguide core 400comprises low-contrast region 402, taper region 404, and high-contrastregion 406. Low-contrast region 402, taper region 404, and high-contrastregion 406 are formed in core layer 408 using accelerator-layertapering, as described above. Core layer 408 is disposed on conventionallower cladding 410.

Taper region 404 includes first taper region 412 and second taper region414, each of which has a different taper angle. In each of low-contrastregion 402 and high-contrast region 406, surface waveguide core 400 is aridge of stoichiometric silicon nitride having a substantiallyrectangular cross-sectional shape having a thickness that is typicallywithin the range of a few nm to approximately 300 nm and a width that istypically within the range of a few nm to tens of microns. In someembodiments, core 400 has a different shape, such as square, irregular(e.g., a “u” shape, “T” shape, etc.). FIG. 4 depicts surface waveguidecore 400 after its thickness has been tapered but prior to the removalof mask layer 418 and accelerator layer 416. Waveguide core 400 is alsodepicted prior to its lateral definition.

In forming surface waveguide core 400, mask layer 418 is first formed onthe surface of accelerator layer 416 and patterned to define opening420, wedge 422, and field region 424. Opening 420 defines low-contrastregion 402. Each of the sides of wedge 422 form angle Φ1 relative toline 426 and 02 relative to propagation axis 428. Line 426 is a linenormal to optical propagation axis 428, as shown. Field region 424protects second taper region 414 and high-contrast region 406 in thesame manner as is described above and with respect to one-dimensionalaccelerator-layer tapering.

Wedge 422 protects core layer 408 and accelerator layer 416 fromvertical attack during the taper etch that forms taper region 404;however, accelerator layer 416 enables accelerator-layer etching of thecore layer to proceed along three directions—the z-direction, direction432, and direction 434, as shown. As a result, accelerator layer 416 isetched laterally at a faster rate in first taper region 412 than insecond taper region 414, resulting in a more gradual tapering of corelayer 408 in first taper region 412 than in second taper region 414.Iso-height profiles 430 indicate vertical height changes of 10 nm. Themore gradual height change in first taper region 412 defines asubstantially linear slope having an angle θ2 with respect to theoriginal top surface of core layer 408, while the more rapid heightchange in second taper region 414 defines a substantially linear slopehaving an angle θ3 with respect to the original top surface of corelayer 408. Boundary 436 denotes an approximate transition between firsttaper region 412 and second taper region 414. Boundary 438 denotes anapproximate transition between second taper region 414 and high-contrastregion 406.

The value of θ3 depend on the relative etch rates of accelerator layer416 and core layer 408, as described above and with respect to θ1 ofFIG. 2C. The values of θ2 and θ3, however, are also dependent upon angleΦ1 of wedge 422, as follows:

$\begin{matrix}{{\theta_{2} = {\arctan\left( {\frac{{ER}\; 1}{{ER}\; 2} \cdot {\cos({\Phi 1})}} \right)}},} & (2) \\{\theta_{3} = {{\arctan\left( \frac{{ER}\; 1}{{ER}\; 2} \right)}.}} & (3)\end{matrix}$

It can be seen from this equation that the magnitude of angle θ2 isinversely dependent on wedge angle Φ1.

FIG. 5A depicts a plot of taper profile for an exemplary spotsizeconverter having a double-angle taper region. Plot 500 shows thethickness of a taper region of a core layer formed using a wedge 422having angle Φ1 of approximately 85°. As cos(85°) is approximately 1/10,the angles θ2 and θ3 have this ratio. In taper region 412, taper angleθ2 is approximately 0.001°, while in taper region 414, taper angle θ3 isapproximately 0.010°. Boundary 436 denotes the approximate transitionbetween angles θ2 and θ3.

FIGS. 5B and 5C depict plots of a mode profile angles induced by anexemplary double-angle taper region and a single-angle linear taperregion, respectively.

Plot 508 shows the mode profile angle, Ψ, induced by the taper angle ofa double-angle linear taper having taper angles θ2 and θ3 of 0.001° and0.010°, respectively for TE polarized light at 1550 nm. For comparison,plot 512 shows the mode profile angle, Ψ, induced by the taper angle ofa simple linear taper for TE polarized light at 1550 nm. A comparison ofplots 508 and 512 shows that the angle of the mode profile induced bythe double-angle taper region is improved over that of the simple lineartaper region.

As disclosed in the parent application, the techniques used to definethe double-angle taper described above can also be used to define ataper having a non-linear, relatively complex vertical profile, such asa ramp having a steadily curving or substantially sinusoidal profile.Such layers can be advantageously used in the core and/or claddinglayers of a transition region of a spot-size converter, as they canfacilitate an adiabatic transition from one guided-mode profile toanother.

FIGS. 6A-B depict schematic drawings of side and top views,respectively, of a spotsize converter having a substantiallysinusoidally tapered core layer in accordance with an illustrativeembodiment of the present invention. Spotsize converter 600 compriseslow-contrast region 602, taper region 604, and high-contrast region 606.In each of these regions, spotsize converter 600 includes a waveguidestructure comprising lower cladding 608, core layer 610, and uppercladding 612. The thickness of core layer 610 varies, from h3 at firstend 614 to h4 at second end 616, as a substantially sinusoidal functionof position along the z-direction within taper region 604, as describedbelow.

Low-contrast region 602 and taper region 604 are formed by tapering corelayer 608 using accelerator-layer tapering, as described above.

FIG. 7 depicts operations of a method suitable for forming a spotsizeconverter in accordance with the illustrative embodiment. Method 700begins with operation 701, wherein core layer 610 is formed on lowercladding 608.

FIGS. 8A-D depict schematic drawings of views of spotsize converter 600at different points in its fabrication.

Lower cladding 608 is a conventional lower cladding layer having athickness and refractive index suitable for use with core layer 608. Inthe illustrative embodiment, lower cladding 608 is a layer of thermallygrown silicon dioxide having a thickness within the range of 5 micronsto 50 microns, and preferably 15 microns. It will be clear to oneskilled in the art that the material and thickness of lower cladding 608are matters of design and that any practical thickness and/or materialcan be used.

Core layer 610 is a layer of stoichiometric silicon nitride having athickness, h3, within the range of approximately 50 nm to approximately300 nm. In the illustrative embodiment, core layer 610 has a thicknessof approximately 220 nm. Typically, core layer 610 is grown on lowercladding 608 using Low-Pressure Chemical Vapor Deposition (LPCVD);however, one skilled in the art will recognize that any suitable methodcan be used to form core layer 610.

At operation 702, accelerator layer 802 is formed on surface 806 of corelayer 610.

At operation 703, mask layer 804 is formed on surface 808 of acceleratorlayer 802 and patterned to define opening 810, shaped region 812, andfield region 814.

FIGS. 8A-B depict schematic drawings of top and side views,respectively, of nascent spotsize converter 600 after formation of masklayer 804. FIG. 8B depicts a cross-sectional view through line a-a ofFIG. 8A, as indicated.

Opening 810 defines the area of core layer 610 in which low-contrastregion 602 is defined. Opening 810 includes sides 816 and 818 thatextend from tip 824 to end 826, where shaped region 812 abuts fieldregion 814. Sides 816 and 818 define the width, Δ(z), of shaped region812, which typically increases monotonically from tip 824 to end 826.Each of sides 816 and 818 has a shape that gives rise to a desiredthickness taper profile for core layer 610 in transition region 604. Theshape of sides 816 and 818 is calculated from the desired verticalprofile of transition region 804.

At each point along the z-direction, each of sides 816 and 818 forms aninstantaneous angle Φ relative to line 822, which is a line drawn normalto propagation axis 820 at that point (i.e., the line aligned with thex-direction at the given z, as shown). This instantaneous angle definesthe shape of opening 810.

FIG. 9 depicts operations of a method suitable for determining the shapeof opening 810 in accordance with the illustrative embodiment of thepresent invention. Method 900 begins with operation 901, wherein thedesired mode-field profile of a light signal in low-contrast region 602is determined. It should be noted that the mode-field profile is definedby the mode-field diameters in both the x- and y-directions for eachpolarization of the light signals (e.g., TE and TM, right- and left-handcircular, etc.). One skilled in the art will recognize that themode-field profile in a surface waveguide is based on several factors,including the materials of the core and cladding of the waveguide, thevertical and lateral dimension (i.e., width) of the waveguide, and thewavelength of the light.

At operation 902, the desired mode-field profile of the light signal inhigh-contrast region 606 is determined.

At operation 903, an estimate of a desired thickness profile, h(z), isdetermined for core layer 610 in transition region 604. In theillustrative embodiment, the desired thickness profile approximates asine-bend shape and is described by:

$\begin{matrix}{{{h(z)} = {{\frac{O_{sine}}{L_{sine}}z} - {\frac{O_{sine}}{2\pi}{\sin\left( {\frac{2\pi}{L_{sine}}z} \right)}}}},} & (4)\end{matrix}$where L_(sine) is the length, L2, of transition region 604 along thez-direction, and O_(sine)=(h1−h2)/2. In some embodiments, the desiredthickness profile, h(z), is other than a sine-bend shape (e.g., anexponential function, etc.). Typically, the desired thickness profile intransition region 604 is based on the application for which spotsizeconverter 600 is intended.

At operation 904, a spline interpolation is performed to determine asmooth interpolation between the mode-field profiles in the low-contrastand high-contrast regions. The mode-field profile in transition region604 can be described by a numerical function MFD(h(z)). In someembodiments, MFD(h(z)) is calculated for several intermediatethicknesses along transition region 604 such that the splineinterpolation provides an MFD(h(z)) that is a substantially smoothnumerical function.

At operation 905, a mode-profile-angle function Ψ(z) suitable forgenerating the result of the spline interpolation is calculated based onMFD(h(z)) and Equations (1) and (2) above, as well as the length, L2, oftransition region 604. It should be noted that the mode-profile angle Ψindicates the rate at which the mode profile changes along thez-direction.

At operation 906, taper-angle function θ(z) is calculated so as to giverise to the desired mode-profile-angle function Ψ(z). The instantaneoustaper-angle 9 is defined as the angle formed, at any given z, betweenthe tangent to the top surface of core layer 610 and a line parallel toa horizontal plane (e.g., the top surface of lower cladding 608, asshown in FIG. 8D).

At operation 907, etch-front-angle function φ(z) is defined for each ofsides 816 or 818 so as to give rise to taper-angle function θ(z).Etch-front-angle function φ(z) dictates the etch-front angle at eachpoint on sides 816 and 818 for each point z along shaped region 812. Forthe purposes of this Specification, including the appended claims, theterm “etch-front angle” is defined as the magnitude of the angle formedbetween a line drawn normal to the propagation axis at a point z and aline drawn tangent to a side of a shaped region at that z.Etch-front-angle function φ(z) determines the magnitude of the distancebetween each of sides 816 and 818 and propagation axis 820 (i.e., thewidth of shaped region 812) from tip 824 to end 826.

Finally, at operation 908, the shape of opening 810 is defined such thatsides 816 and 818 are characterized by etch-front-angle function φ(z).

FIGS. 10A-B depict plots of the magnitude of etch-front angle φ as afunction of distance, z, for taper regions having lengths of 2 mm and 1mm, respectively.

Returning now to method 700, at operation 704, nascent spotsizeconverter 600 is exposed to a suitable etchant (e.g., etchant 210) attime t(0). As discussed above and with respect to FIGS. 2A-C, theetchant is selected such that it etches the material of acceleratorlayer 802 at a faster rate than the material of core layer 610. As aresult, accelerator layer 802 is removed quickly in region 602 and theetchant begins to etch the accelerator layer laterally along thez-direction, as well as along directions normal to sides 816 and 818,thereby undercutting mask layer 804.

As the etchant undercuts mask layer 804, the etch fronts from eachexposed edge of shaped region 812 begin to meet. Since the lateralextent of shaped region 812 is a function of z, the duration of theexposure of surface 806 to the etchant is a function of both φ(z) and z.As a result, the thickness of core layer 610 in shaped region 812 isbased on t, φ(z), and z. Along the z-direction, therefore, the profileof core layer 610 can be selected as nearly any desired monotonicallyincreasing function of z, by judicious selection of φ(z). In theillustrative embodiment, this profile is substantially a portion of asinusoid; however, it will be clear to one skilled in the art, afterreading this Specification, how to specify, make, and use taperedregions having any suitable substantially monotonically changingvertical profile, including linear, piecewise linear, non-linear,sinusoidal, curved, irregular, and the like.

At operation 705, the etching of core layer 610 is stopped at time t(1).Time t(1) is selected based on the etch rate of the material of layer110 in etchant 210, initial thickness, h3, final thickness, h4, and thedesired length, L2, of taper region 604.

FIGS. 8C and 8D depict top and side views, respectively, of nascentspotsize converter 600 after the tapering of core layer 610. In FIG. 8C,iso-height lines 828 indicate height changes of approximately 20 nm.

FIGS. 11A-B depict plots of the thickness of exemplary core layers 610as a function of distance, z, for taper regions having lengths of 2 mmand 1 mm, respectively. Plots 1100 and 1102 show the thickness of corelayer 610 from second end 616 to first end 614, for a core layer havingan initial thickness, h3, of 220 nm and a final thickness, h4, inlow-contrast region 602 of approximately 65 nm.

FIGS. 11C-D depict plots of the taper angle, θ, of exemplary core layers610 as a function of distance, z, for taper regions having lengths of 2mm and 1 mm, respectively. Plots 1104 and 1106 show the instantaneousangle of the top surface of core layer 610 from second end 616 to firstend 614, for a core layer having an initial thickness, h3, of 220 nm anda final thickness, h4, in low-contrast region 602 of approximately 65nm.

At operation 706, accelerator layer 802 and mask layer 804 are strippedfrom nascent spotsize converter 600.

At operation 707, core layer 610 is patterned to define core 618. Inhigh-contrast region 606, core 618 has width w1, which is within therange of a few nanometers to a few tens of microns and typically about 1micron. In low-contrast region 602, core 618 has width w2, which is alsowithin the range of a few nanometers to a few tens of microns. In theillustrative embodiment, w1 is approximately 1 micron and w2 isapproximately 65 nm. In transition region 604, the width of core 618 isa function of z. In some embodiments, the width function w(z) isdetermined in analogous fashion to that described above and with respectto FIG. 9. Typically, w(z) changes monotonically along transition region604. In the illustrative embodiment, wherein transition region 604 has athickness that approximates a sine-bend shape, w(z) is defined as:

$\begin{matrix}{{{w(z)} = {{\frac{O_{sine}}{L_{sine}}z} - {\frac{O_{sine}}{2\pi}{\sin\left( {\frac{2\pi}{L_{sine}}z} \right)}}}},} & (5)\end{matrix}$where L_(sine) is the length, L2, of transition region 604 along thez-direction, and O_(sine)=(w1−w2)/2.

It will be clear to one skilled in the art, after reading thisSpecification, how to define a suitable function, w(z), based on theapplication for which spotsize converter 600 is intended. In someembodiments, core 618 has the same width in all of regions 602, 604, and606.

In some embodiments, core 618 comprises a composite core having an innercore of a first material (e.g., silicon dioxide) surrounded by an outercore of a second material (e.g., silicon nitride). In some embodiments,core 618 comprises a composite core having a central core of a firstmaterial (e.g., silicon dioxide) that is disposed between lower andupper core layers comprising a second material (e.g., silicon nitride).A composite core is characterized by an effective refractive index thatis determined by the materials used as well as the geometry of the coredesign. As a result, these factors also affect the effectiverefractive-index contrast of a composite-core waveguide, which is alsoaffected by other factors, such as core and cladding dimensions, coreand cladding materials, and the like.

In some embodiments, the transition region wherein the lateral dimensionof core 618 changes is not aligned along the z-direction with thetransition region wherein the thickness of core 618 changes. In otherwords, in some embodiments, spotsize converter 600 includes two separatetransition regions—one for the thickness of core 618 and another for thelateral dimension of core 618.

At operation 708, upper cladding 612 is formed on core layer 610 inconventional fashion to complete the fabrication of spotsize converter600. Upper cladding 612 is normally a layer of silicon oxide (e.g.,silicon dioxide, silicon monoxide, etc.) formed via LPCVD depositionusing a precursor gas such as tetraethyl orthosilicate (TEOS), whichresults in a conformal oxide layer.

Upper cladding 612 typically has a thickness within the range ofapproximately 1 micron to approximately 30 microns. In the illustrativeembodiment, upper cladding has a thickness of approximately 15 microns.In some embodiments, upper cladding 612 has a thickness that is lessthan 1 micron. In some embodiments, upper cladding 612 is not present.

Although the illustrative embodiment includes a waveguide having lowerand upper cladding layers that have substantially uniform thicknessthroughout, it will be clear to one skilled in the art, after readingthis Specification, how to specify, make, and use alternativeembodiments of the present invention wherein at least one of the upperand lower cladding layers is tapered in similar fashion to the manner inwhich core layer 610 is tapered, as described above, such that one orboth of these cladding layers has a thickness and/or width that changesalong the propagation direction in at least a portion of a waveguide.

FIGS. 12A and 12B depict plots of a mode profile induced by exemplarysinusoidal taper regions having lengths of approximately 2 mm and 1 mm,respectively.

Plot 1200 shows the mode profile angle, Ψ, along transition region 604from second end 616 to first end 614, where the length of the transitionregion, L2, is 2 mm. Traces 1202 and 1204 show the mode profile anglefor TE and TM polarized light, respectively, at 1550 nm.

Plot 1206 shows the mode profile angle, Ψ, along transition region 604from second end 616 to first end 614, where the length of the transitionregion, L2, is 1 mm. Traces 1208 and 1210 show the mode profile anglefor TE and TM polarized light, respectively, at 1550 nm.

Although the illustrative embodiment comprises a spotsize converterhaving a transition region including a core layer having a sinusoidalthickness profile, it will be clear to one skilled in the art, afterreading this Specification, how to specify, make, and use spotsizeconverters that include a core layer having any suitable substantiallychanging vertical profile, including linear, piecewise linear,non-linear, curved, irregular, monotonically changing, non-monotonicallychanging, exponential, and the like.

In some embodiments, core layer 610 is formed such that it has a taperangle that changes in substantially constant fashion along transitionregion 604 (neglecting changes that might occur in the immediatevicinity of first end 614 or second end 616). Such a thickness profileaffords these embodiments with additional advantages, such as theability to distribute vertical bending loss (induced by peaks in thetaper angle) evenly along the length of the transition region.

In some embodiments, core layer 610 is formed as part of a waveguidestructure such that the value of the mode-profile-angle, Ψ, of thewaveguide remains substantially constant along the length of transitionregion 604. In some of these embodiments, the thickness of core layer610 increases substantially exponentially along the length of transitionregion 604.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

What is claimed is:
 1. A planar-lightwave circuit (PLC) including afirst surface waveguide, the first surface waveguide comprising: a firstcladding layer comprising a first material characterized by a firstrefractive index; a second cladding layer comprising a second materialcharacterized by a second refractive index; and a first layer comprisinga third material characterized by a third refractive index that isgreater than each of the first and second refractive indices, the firstlayer being between the first and second cladding layers, and the firstlayer having a first region, second region, and third region that isbetween the first region and second region, wherein the third regionabuts the first region at a first point along a first axis, and whereinthe third region abuts the second region at a second point along thefirst axis; wherein the first layer has a first thickness in the firstregion, a second thickness in the second region, and a third thicknessin the third region that changes between the first thickness at thefirst point and the second thickness at the second point according to asubstantially sinusoidal function of position, z, along the first axis;and wherein the first surface waveguide has a first mode-field profilein the first region, a second mode-field profile in the second region,and a third mode-field profile, MFD(h(z)), that changes between thefirst mode-field profile and second mode-field profile between the firstpoint and the second point, MFD(h(z)) being characterized by asubstantially sinusoidal function of position, z, along the first axis.2. The PLC of claim 1 wherein the third thickness changes insubstantially sinusoidal fashion along the first axis between the firstpoint and the second point.
 3. The PLC of claim 1 wherein the firstsurface waveguide has a first width in the first region, a second widthin the second region, and a third width in the third region that changesmonotonically along the first axis from the first point to the secondpoint.
 4. The PLC of claim 1 wherein the third thickness along the firstaxis between the first point and second point is characterized by onehalf period of a sinusoidal function.
 5. The PLC of claim 1 wherein thefirst layer is characterized by a taper-angle at each point along thefirst axis between the first point and second point, and wherein thetaper angle increases at a constant rate along the first axis from thefirst point to the second point.
 6. The PLC of claim 3 wherein the thirdwidth changes non-linearly along the first axis from the first point tothe second point.
 7. A planar-lightwave circuit (PLC) that includes afirst surface waveguide, the first surface waveguide comprising a core,wherein first surface waveguide comprises: a first region in which thecore has a first thickness, wherein, in the first region, the firstsurface waveguide is characterized by a first refractive-index contrastthat is based on the first thickness; a second region in which the corehas a second thickness, wherein, in the second region, the first surfacewaveguide is characterized by a second refractive-index contrast that isbased on the second thickness; and a third region that is between thefirst region and the second region and abuts the first region at a firstpoint along a first axis and abuts the second region at a second pointalong the first axis, wherein the surface waveguide has a thirdrefractive-index contrast that is based on a third thickness of thecore, wherein the third refractive-index contrast changes between thefirst refractive-index contrast and the second refractive-index contrastaccording to a substantially sinusoidal function of position between thefirst point and the second point.
 8. The PLC of claim 7 wherein thefirst surface waveguide includes a core layer comprising a firstmaterial, the core layer having the first thickness in the first region,the second thickness in the second region, and a third thickness in thethird region that changes continuously and non-linearly between thefirst thickness at the first point and the second thickness at thesecond point according to a sinusoidal function of position, z, alongthe first axis.
 9. The PLC of claim 8 wherein the third thickness ischaracterized by one half period of a sinusoidal function.
 10. The PLCof claim 8 wherein the first layer is characterized by a taper-angle ateach point along a first axis between the first point and second point,and wherein the taper angle changes according to a substantiallysinusoidal function of position along the first axis from the firstpoint to the second point.
 11. A planar-lightwave circuit (PLC)including a first surface waveguide, the first surface waveguidecomprising: a first cladding layer comprising a first materialcharacterized by a first refractive index; a second cladding layercomprising a second material characterized by a second refractive index;and a first layer comprising a third material characterized by a thirdrefractive index that is greater than each of the first and secondrefractive indices, the first layer being between the first and secondcladding layers, and the first layer having a first region, secondregion, and third region that is between the first region and secondregion, wherein the third region abuts the first region at a first pointalong a first axis, and wherein the third region abuts the second regionat a second point along the first axis; wherein the first layer has afirst thickness in the first region, a second thickness in the secondregion, and a third thickness in the third region that changes betweenthe first thickness and the second thickness along the first axisbetween the first point and the second point according to asubstantially sinusoidal function of position along the first axis. 12.The PLC of claim 11 wherein the first surface waveguide has a firstmode-field profile in the first region, a second mode-field profile inthe second region, and a third mode-field profile, MFD(h(z)), thatchanges continuously and non-linearly between the first mode-fieldprofile and second mode-field profile between the first point and thesecond point, MFD(h(z)) being characterized by a substantiallysinusoidal function of position, z, along the first axis.
 13. The PLC ofclaim 12 wherein the third thickness is characterized by one half periodof a sinusoidal function.
 14. The PLC of claim 11 wherein the firstlayer is characterized by a taper-angle at each point along a first axisbetween the first point and second point, and wherein the taper angleincreases at a constant rate along the first axis from the first pointto the second point.
 15. The PLC of claim 11 wherein the first surfacewaveguide has a third refractive-index contrast that changes between thefirst refractive-index contrast and the second refractive-index contrastaccording to a substantially sinusoidal function of position between thefirst point and the second point.